July 10, 2010

Expected Value — how to tell if a house is a good deal

Last quarter, I took an econometrics course. I learned a lot about the theory of how to do linear regressions, and use those regressions to learn things about any commodity. I chose to use my knowledge to look at house prices for houses like mine, and learned something I wish I knew years ago, when I bought my house.

I should have done an expected value calculation before buying a house! It would have saved me thousands, by telling me that housing was overpriced, by how much, and more importantly — how long it can remain that way. I got lucky — I didn’t buy at the top, and my area didn’t have rampant price inflation, so things could have been much worse. However, I didn’t know to look at expected value, barely knew what it was, and otherwise used the wrong method to determine when/if to buy a house.

Benefits of expected value:

Know if this house is a good deal or not. You want to sell when the market price is above the expected value, and buy when below.

Learn the appreciation function of your house. Are you earning 5% a year on it? 6%? Losing money? Expected value tells you.

Learn if your loan is a good deal. How much of your mortgage is really going into equity?

The time-linear definition of expected value

A lot of business books talk about expected value — but they mean it in terms of risk theory. Risk theory defines expected value as the probability of some event times the magnitude of the loss/payoff. However, I’m referring to temporal expected value, not risk expected value. In this context of home prices, expected value is the price of the house under normal economic conditions. That means no bubbles, no crashes. Just the price as it would ordinarily be. No, this isn’t the inflation adjusted price, as there’s other factors besides inflation involved. No, this isn’t a mixed mode housing equation that real-estate economists like to use, because that’s more like a forecast. In more specific terms, its the coefficient of the price appreciation function in log scale. It tells you, “This house is worth XXX dollars under normal conditions.”

How does expected value differ from market price?

Market price is the price you would pay right now to sell/buy this house. It changes, surprisingly often and quickly. Expected value is constant, and its a theoretical price. It’s the projected market price of the home under normal macro-economic conditions. You can go to websites like Zillow to learn the market price, but no one tells you the expected value. With expected value, you can learn how much money you would make/lose buying or selling this house, you can learn how much the house value will change over time, and you can learn if your loan is a good or bad deal relative to the house.

Why does no-one state the expected value?

The problem with expected value is that no transactions occur at it — it’s a theoretical price. People buy and sell houses at Market prices. People who make commissions, make them by selling you a house or by helping you buy one. The few people who know how to do the regressions to learn this value can get paid big bucks for doing them for a REIT, wealthy bank, investment firm, etc… Ordinary homebuyers won’t know how, and the knowledge it gives you is “should I buy this house? Should I sell this house?” No-one makes any money helping you figure that out. They only make money if you do buy/sell a house. If you want to know what the expected value is, you’ll have to figure it out yourself. Luckily, you can do it yourself.

How to do the calculations

I use a really easy method for expected value calculations. I go to the county assessor and lookup comparable home sale history over the last few decades. King County’s records are all online, so in Seattle, it’s easy enough to find them. Once I’ve sampled my comparables, I convert everything to log scale and do a simple linear regression on them. This gives me a good proxy for expected value. You can do this using the regression function of Excel, though I prefer to use EViews, as it gives me regression diagnostic data that tells me if the regression is any good. You can see my previous post to see the process in action.

In more detail, you create the following table with similar homes. Defining similar homes is tricky — I used geography and size as my methods, removing houses with special terrain features. It takes a while to do it, but you can see my SQL query for it in the link to my previous post:

House Price, Quarter, Year, Log House price

Log house price is a formula — you take the log of house price and put it here. You then take this data and compute the average of log house price for each quarter.

So, you get something that looks kind of like this:

Avg Log House Price, Quarter, Year — with only 1 value for each quarter/year.

Then you run a time regression function in Excel, Eviews, R, whatever — and viola, you know expected value for a similar house. You can then find the expected log for right now, and make it a power of e( the irrational number e is roughly 2.718 ). This tells you the expected price right now. You take the current market price, and see if it is above or below this expected price. This is how much profit/loss you would make if the economy were in normal conditions. Right now, in some areas, this number is larger than the house price itself — a screaming good deal — if you can wait out this recession. Prices will remain steady or keep falling in many area, even though they are low. We’ve been lower before — 1982 and 1987 were more serious corrections than now, indicating there’s still room to fall. But you’ll never know when the bottom hits — you just have to know that when things turn around, how high they will go.